It is known in the air valve art to provide air valves with valve spools operated by solenoids. Heretofore, in four-way directional flow control air valves which employed a valve spool directly operated by a solenoid, the valve spool was stopped by a suitable stop of some sort in the solenoid cover. Such prior art direct solenoid operated valve spool structures included many tolerances in the manufacture of the various parts of the solenoid, including the cover and the cover gasket. It was impossible, with such prior art structure, to provide a direct solenoid operated valve with minimum tolerance accumulation so as to provide an accurate short stroke of a solenoid to impart a similar accurate short stroke to a four-way valve spool. In such prior art direct solenoid operated directional flow control air valves it was also necessary to account for the various tolerances in manufacturing the valve spool to provide a desired valve spool travel.